Finite Group Databasebeta

← #23769185

Subgroups — #23769185

Order 10112.

526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579143C211yesmaximal, characteristic
2C2×C4⋊C4×D79C211yesmaximal, characteristic, complemented
3#19098503C211yesmaximal, characteristic, complemented
4#19098501C211yesmaximal, characteristic, complemented
5#19098499C211yesmaximal, characteristic, complemented
6#19098496C212yesmaximal, complemented
7#19098491C212yesmaximal, complemented
8#19098439C212yesmaximal
9#19098434C212yesmaximal, complemented
10#19098425C211yesmaximal, characteristic, complemented
11#399×C79C211yesmaximal, characteristic, complemented
12C22×C22⋊D79C2211yescharacteristic
13C22×C4×D79C2211yescharacteristic
14C22×C4×D79C2212yes—
15#14579143—24no—
16C2×C4⋊Dic79C2211yescharacteristic
17C2×C4⋊Dic79C2211yescharacteristic
18C2×Dic79⋊C4C2212yes—
19C2×Dic79⋊C4C2211yescharacteristic
20C2×Dic79⋊C4C2212yes—
21C4⋊C4×D79—24no—
22C2×C22⋊Dic79C2211yescharacteristic
23C2×C22⋊Dic79C2212yes—
24C2×(C2×D79)⋊C4C2212yes—
25C2×(C2×D79)⋊C4C2211yescharacteristic
26C79⋊#95C2212yes—
27C79⋊#95C2211yescharacteristic
28C79⋊#95C2212yes—
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C2×C4⋊C4×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2212yes—
34C2×C22⋊C4×C79C2211yescharacteristic
35C2×C22⋊C4×C79C2212yes—
36#95×C79C2211yescharacteristic
37C23×D79C2311yescharacteristic
38C2×C22⋊D79—22no—
39C2×C22⋊D79—24no—
40C22×Dic79C2311yescharacteristic
41C22×Dic79C2312yes—
42C22×Dic79C2311yescharacteristic
43C22×Dic79C2312yes—
44C22×Dic79C2311yescharacteristic
45C2×C4×D79—24no—
46C2×C4×D79—24no—
47C2×C4×D79—42no—
48C2×C4×D79—42no—
49C2×C4×D79D414yes—
50C4⋊Dic79—22no—
51C4⋊Dic79—22no—
52Dic79⋊C4—24no—
53Dic79⋊C4—22no—
54Dic79⋊C4—42no—
55C22⋊Dic79—22no—
56C22⋊Dic79—42no—
57(C2×D79)⋊C4—22no—
58(C2×D79)⋊C4—24no—
59C24×C79C2311yescharacteristic
60C22×C4×C79C2312yes—
61C22×C4×C79C2312yes—
62C22×C4×C79C2311yescharacteristic
63C22×C4×C79C2311yescharacteristic
64C4⋊C4×C79—22no—
65C4⋊C4×C79—42no—
66C22⋊C4×C79—22no—
67C22⋊C4×C79—42no—
68C23×C79—21no—
69C23×C79—22no—
70C23×C79—22no—
71C23×C79—21no—
72C23×C79—21no—
73C23×C79C2411yescharacteristic
74C22×D79—22no—
75C22×D79—21no—
76C22×D79—21no—
77C22×D79C2×D412yes—
78C22×D79#4114yes—
79C2×C4×C79—22no—
80C2×C4×C79—21no—
81C2×C4×C79—22no—
82C2×C4×C79—22no—
83C2×C4×C79—22no—
84C2×C4×C79—22no—
85C2×C4×C79—22no—
86C2×C4×C79—22no—
87C2×C4×C79—22no—
88C2×C4×C79C2×D412yes—
89C22⋊D79—44no—
90C2×Dic79—22no—
91C2×Dic79—21no—
92C2×Dic79—22no—
93C2×Dic79—21no—
94C2×Dic79—22no—
95C2×Dic79—22no—
96C2×Dic79—22no—
97C2×Dic79—22no—
98C2×Dic79—22no—
99C2×Dic79—21no—
100C2×Dic79—21no—
101C2×Dic79—22no—
102C2×Dic79C2×D412yes—
103C4×D79—28no—
104C4×D79—48no—
105C22×C79—41no—
106C22×C79—41no—
107C22×C79—41no—
108C22×C79—42no—
109C22×C79—42no—
110C22×C79C22×D411yescharacteristic
111C22×C79C2×#4112yes—
112C22×C79H(5,𝔽2)12yes—
113C22×C792−1+411yescharacteristic
114C22×C792−1+411yescharacteristic
115C2×D79—22no—
116C2×D79—22no—
117C2×D79—24no—
118C2×D79—24no—
119C2×D79#12314yes—
120C4×C79—22no—
121C4×C79—41no—
122C4×C79—42no—
123C4×C79—42no—
124Dic79—22no—
125Dic79—41no—
126Dic79—42no—
127Dic79—41no—
128Dic79—42no—
129C2×C79—81no—
130C2×C79C2×#12311yescharacteristic
131C2×C79#53511yescharacteristic
132C2×C79#53611yescharacteristic
133C2×C79#53912yes—
134C2×C79#53912yes—
135D79—24no—
136#2623—791nomaximal, Sylow
137C79#262311yescharacteristic, complemented, Sylow
138C2×#123—791no—
139C22×C4⋊C4—791no—
140#400—791no—
141#400—791no—
142#399—791no—
143#399D7911yescharacteristic, complemented
144#398—792no—
145#397—792no—
146#386—792no—
147#385—792no—
148#381—791no—
149C22×D4—791no—
150C23×C4—792no—
151C23×C4—791no—
152#123—1584no—
153C2×C4⋊C4—792no—
154C2×C4⋊C4—792no—
155C2×C4⋊C4—791no—
156C2×C4⋊C4—791no—
157C2×C4⋊C4—791no—
158C2×C4⋊C4—1584no—
159C2×C4⋊C4C2×D7911yescharacteristic
160C2×C4⋊C4C2×D7912yes—
161C2×C22⋊C4—792no—
162C2×C22⋊C4—791no—
163C2×C22⋊C4—791no—
164C2×C22⋊C4—792no—
165C2×C22⋊C4C2×D7911yescharacteristic
166C2×C22⋊C4C2×D7912yes—
167#95—792no—
168#95—791no—
169#95—792no—
170#95—792no—
171#95—792no—
172#95—792no—
173#95C2×D7911yescharacteristic
174C24—791no—
175C24C22×D7911yescharacteristic
176C2×D4—1582no—
177C2×D4—1584no—
178C22×C4—3162no—
179C22×C4—3162no—
180C22×C4—791no—
181C22×C4—794no—
182C22×C4—792no—
183C22×C4—791no—
184C22×C4—791no—
185C22×C4—792no—
186C22×C4—1584no—
187C22×C4—1584no—
188C22×C4C22×D7912yes—
189C22×C4C22×D7912yes—
190C22×C4C22×D7911yescharacteristic
191C22×C4C22×D7911yescharacteristic
192C4⋊C4—22no—
193C4⋊C4—42no—
194C4⋊C4—3162no—
195C4⋊C4—1584no—
196C4⋊C4—1582no—
197C4⋊C4—1582no—
198C4⋊C4—1582no—
199C22⋊C4—22no—
200C22⋊C4—42no—
201C22⋊C4—3162no—
202C22⋊C4—1584no—
203C22⋊C4—1582no—
204C22⋊C4—1582no—
205C23—22no—
206C23—22no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—794no—
211C23—792no—
212C23—1582no—
213C23—1581no—
214C23—1581no—
215C23C23×D7911yescharacteristic
216D4—3164no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—3168no—
227C2×C4—792no—
228C2×C4—1588no—
229C2×C4—1582no—
230C2×C4—1582no—
231C2×C4—1582no—
232C2×C4—1582no—
233C2×C4—1582no—
234C2×C4—1581no—
235C2×C4—1581no—
236C2×C4—1582no—
237C2×C4—1581no—
238C2×C4—1582no—
239C2×C4—1581no—
240C2×C4—1582no—
241C2×C4D4×D7912yes—
242C22—41no—
243C22—42no—
244C22—42no—
245C22—41no—
246C22—41no—
247C22—794no—
248C22—1582no—
249C22—1584no—
250C22—1584no—
251C22—1582no—
252C22C2×D4×D7911yescharacteristic
253C22#41×D7912yes—
254C22#1457920612yes—
255C22#1457920811yescharacteristic
256C22#1457920911yescharacteristic
257C4—22no—
258C4—42no—
259C4—42no—
260C4—41no—
261C4—3161no—
262C4—3162no—
263C4—3161no—
264C4—3162no—
265C4—1582no—
266C2—81no—
267C2—1584no—
268C2#123×D7911yescharacteristic
269C2#1909912611yescharacteristic
270C2#1909913611yescharacteristic
271C2#1909915612yes—
272C2#1909915912yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#399×C79C2
prime radicalC22×C22⋊D79C22
hypercenter#399D79
hypocenterC79#2623
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #399

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C4⋊C4×D79C2semidirect
3. #19098503C2semidirect
4. #19098501C2semidirect
5. #19098499C2semidirect
6. #19098496C2semidirect
7. #19098491C2semidirect
9. #19098434C2semidirect
10. #19098425C2semidirect
11. #399×C79C2semidirect
137. C79#2623semidirect
143. #399D79semidirect